Simplify ( sixth root of 8a^5b^7)/( sixth root of 2a^2b^3)

$\frac{\sqrt[6]{8 a^{5} b^{7}}}{\sqrt[6]{2 a^{2} b^{3}}}$

Combine $\sqrt[6]{8 a^{5} b^{7}}$ and $\sqrt[6]{2 a^{2} b^{3}}$ into a single radical.

$\sqrt[6]{\frac{8 a^{5} b^{7}}{2 a^{2} b^{3}}}$

Reduce the expression $\frac{8 a^{5} b^{7}}{2 a^{2} b^{3}}$ by cancelling the common factors.

Factor $2$ out of $8 a^{5} b^{7}$ .

$\sqrt[6]{\frac{2 (4 a^{5} b^{7})}{2 a^{2} b^{3}}}$

Factor $2$ out of $2 a^{2} b^{3}$ .

$\sqrt[6]{\frac{2 (4 a^{5} b^{7})}{2 (a^{2} b^{3})}}$

Cancel the common factor.

$\sqrt[6]{\frac{2 (4 a^{5} b^{7})}{2 (a^{2} b^{3})}}$

Rewrite the expression.

$\sqrt[6]{\frac{4 a^{5} b^{7}}{a^{2} b^{3}}}$

Cancel the common factor of $a^{5}$ and $a^{2}$ .

Factor $a^{2}$ out of $4 a^{5} b^{7}$ .

$\sqrt[6]{\frac{a^{2} (4 a^{3} b^{7})}{a^{2} b^{3}}}$

Cancel the common factors.

Factor $a^{2}$ out of $a^{2} b^{3}$ .

$\sqrt[6]{\frac{a^{2} (4 a^{3} b^{7})}{a^{2} (b^{3})}}$

Cancel the common factor.

$\sqrt[6]{\frac{a^{2} (4 a^{3} b^{7})}{a^{2} b^{3}}}$

Rewrite the expression.

$\sqrt[6]{\frac{4 a^{3} b^{7}}{b^{3}}}$

Cancel the common factor of $b^{7}$ and $b^{3}$ .

Factor $b^{3}$ out of $4 a^{3} b^{7}$ .

$\sqrt[6]{\frac{b^{3} (4 a^{3} b^{4})}{b^{3}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[6]{\frac{b^{3} (4 a^{3} b^{4})}{b^{3} \cdot 1}}$

Cancel the common factor.

$\sqrt[6]{\frac{b^{3} (4 a^{3} b^{4})}{b^{3} \cdot 1}}$

Rewrite the expression.

$\sqrt[6]{\frac{4 a^{3} b^{4}}{1}}$

Divide $4 a^{3} b^{4}$ by $1$ .

$\sqrt[6]{4 a^{3} b^{4}}$